Generalised U-dual solutions in supergravity

TL;DR

This paper introduces a new supergravity solution generation method called generalised U-duality, extending non-abelian T-duality, and demonstrates it with an example leading to AdS3 backgrounds with holographic duals.

Contribution

It develops a novel solution generating technique in supergravity using exceptional geometry, generalising non-abelian T-duality with a 3-algebra structure, and applies it to produce new AdS3 solutions.

Findings

Generated new 11D supergravity solutions from type IIA solutions on a 3-sphere.

Found that the solutions can be viewed as U-folds with M2 and M5 brane charges.

Explicitly constructed a 1/2-BPS solution in the AdS3 limit.

Abstract

We discuss the notion of generalised U-duality as a solution generating technique in supergravity. We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques. These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. We discuss the properties of our resulting new solution, including the possibility of viewing it globally as a U-fold, and its M2 and M5 brane charges. In the extremal case, the new solution admits an AdS${}_3$ limit, which falls into a recently constructed class of M-theory AdS$_{3}$ backgrounds -- this provides a global completion of our solution with a well-defined holographic dual, similar to the global completions of non-abelian T-dual solutions. Our full solution is a 6-vector deformation of this AdS${}_3$ limit. We also explicitly solve the Killing spinor equation in the AdS${}_3$ limit, finding a $\frac{1}{2}$-BPS solution.